Found a scrap of green felt in the junk box. I fired up the antique Singer sewing machine in the attic.
Folded the felt in half around the pump, and sewed up one side and the bottom.
Turned the bag inside-out, so the seam is on the inside.
Installed two little green grommets and a piece of copper wire to close the lid.
I will look for a thin leather thong or shoelace to make a nicer presentation.